Chelsea have made a stuttering start to their title defence with three losses in 10 games to sit in fourth spot, nine points adrift of Manchester City and four behind second-placed United.
They lost 3-0 at AS Roma in the Champions League on Tuesday, while United won 2-0 at home to Benfica, and Courtois said his team mates were determined to bounce back from the setback.
"We will try to get the three points and will give our lives for it on Sunday," Courtois told British media.
"We have to react on Sunday as the Roma defeat was a bad image of ourselves... we must win games like these (United) to remain at the top and close to the other ones (teams)."
Antonio Conte's side have kept only four clean sheets in the Premier League so far this season plus one in four Champions League matches and Courtois knows they have to sort out their defensive problems for United's visit.
"We have to find that balance again and rediscover that mentality of not conceding goals and keeping clean sheets," said the Belgian international.
N'Golo Kante, who has missed Chelsea's last five matches with a hamstring injury, trained with the squad before the Roma clash and could return against United but Courtois said the midfielder would not be pushed into action too early.
"We know how important N'Golo is for us. He is the guy that brings a lot of balance into the team. But we can't push him to play if he doesn't feel ready," said the keeper.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris)
